题目内容
已知向量
的最小值为( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231846141621408.png)
A.![]() | B.6 | C.12 | D.![]() |
B
考点:
专题:计算题.
分析:利用向量垂直的充要条件列出方程求出x,y满足的方程;利用基本不等式得到函数的最值,检验等号何时取得.
解答:解:由已知
?
=0?(x-1,2)?(4,y)=0?2x+y=2
则9
+3
=3
+3
≥2
=2
=2
=6,
当且仅当3
=3
,即x=
,y=1时取得等号.
故答案为:6
点评:本题考查向量垂直的充要条件:坐标交叉相乘相等、考查利用基本不等式求函数的最值需满足的条件:一正、二定、三相等.
专题:计算题.
分析:利用向量垂直的充要条件列出方程求出x,y满足的方程;利用基本不等式得到函数的最值,检验等号何时取得.
解答:解:由已知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614225432.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614240424.png)
则9
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614256230.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614272249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614287295.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614272249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614334588.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614350552.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614459409.png)
当且仅当3
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614287295.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614272249.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823184614506338.png)
故答案为:6
点评:本题考查向量垂直的充要条件:坐标交叉相乘相等、考查利用基本不等式求函数的最值需满足的条件:一正、二定、三相等.
![](http://thumb2018.1010pic.com/images/loading.gif)
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